1. Technical Field
Embodiments of the subject matter disclosed herein generally relate to methods and systems for producing images of a subsurface and, more particularly, to mechanisms and techniques for reducing under-sampling associated noise for reverse time migration three-dimensional angle domain common image gathers.
2. Discussion of the Background
Marine seismic data acquisition and processing generate a profile (image) of the geophysical structure under the seafloor. While this profile does not provide an accurate location for the oil and gas, it suggests, to those trained in the field, the presence or absence of oil and/or gas. Thus, providing a high resolution image of the structures under the seafloor is an ongoing process.
During a seismic gathering process, as shown in FIG. 1, a vessel 10 tows an array of seismic receivers 12 provided on cables 14 that form streamers 16. The streamers may be disposed horizontally, i.e., lying at a constant depth z1 relative to a surface 18 of the ocean. The vessel 10 also tows a sound source assembly 20 that is configured to generate an acoustic wave 22a. The acoustic wave 22a propagates downwards toward the seafloor 24 and penetrates the seafloor until eventually a reflecting structure 26 (reflector R) reflects the acoustic wave. The reflected acoustic wave 22b propagates upwardly until is detected by receiver 12. The recorded data is then processed for producing an accurate image of the subsurface. The processing may include various phases, e.g., velocity model determination, pre-stack, migration, post-stack, etc., which are known in the art and thus, their description is omitted herein.
The availability of wide-azimuth (WAZ) data, together with reverse time migration (RTM), has increased the capability to image complex subsalt structures. The WAZ data provides better illumination of subsalt structures than the narrow azimuth (NAZ) data does. The abundant azimuthal information in WAZ data also produces better noise cancellation due to its higher folds (i.e., the number of recorded signals corresponding to a surveyed point in the subsurface).
For pre-stack depth migration, a common image gather (CIG) is the link to the velocity model building. The conventional CIGs are generated by Kirchhoff migration in the offset domain. Because the RTM provides better images than the Kirchhoff migrations when the structures are complicated (see Zhang, Y. and J. Sun, “Practical issues of reverse time migration: true-amplitude gathers, noise removal and harmonic-source encoding,” First Break, 26, 19-25, 2009), it is necessary to generate CIGs from RTM to enhance the RTM usage of WAZ data process.
To retain the azimuthal information in WAZ data for tomography, the RTM CIGs have to be three dimensional (see Huang et al., “The application of RTM 3D gathers for wide azimuth data in Garden Banks, Gulf of Mexico,” 80th Annual International Meeting, SEG Expanded Abstracts, 3298-3302, 2010). On the other hand, the usage of CIGs for reservoir attribute interpretation, such as amplitude versus angle/azimuth (AVA) analysis, requires amplitude fidelity.
Therefore, there is a need to incorporate the amplitude preserving algorithm in 3D angle-domain CIGs (ADCIGs). Based on the true-amplitude RTM theory, a method to generate 3D ADCIGs has been developed for a general anisotropic medium (see Xu et al., “3D common image gathers from reverse time Migration,” 80th Annual International Meeting, SEG Expanded Abstracts, 3257-3262, 2010), and it has been applied to WAZ data processing (see Huang et al., 2010).
3D ADCIG with RTM is a superior choice for pre-stack imaging in complex geological areas (see Zhang et al., “Angle gathers from reverse time migration,” The Leading Edge, 29, 1364-1371, 2010). The advantage of 3D ADCIGs is that they retain the localized subsurface information with respect to azimuth angles and reflection angles which can be used for velocity inversion, migration quality control, anisotropy model building and AVA analysis. For ADCIGs, the output traces from RTM are indexed by both the subsurface reflection angle θ and the azimuth angle α.
Therefore, the RTM 3D ADCIG migration is in fact a mapping process in five dimensions which maps the WAZ data from a 5D input space (xs, ys, xr, yr, t) to a 5D output space (x, y, z, θ, α), where xs and ys are the coordinates of the source, xr and yr are the coordinates of the receiver, x, y, and z are the coordinates of a migrated point.
However, this technique introduces various challenges to the geophysicists. First, it dramatically increases the numerical cost because of the five dimensional mapping process and the finite difference wave-field propagation. Second, the locations of the sources and receivers are coarsely sampled on the surface and reflections from very near offsets are usually not recorded in marine streamer acquisitions. Thus, this mapping process leads to severe sampling issues. Xu et al. discussed how to reduce the computational cost by introducing a windows anti-leakage Fourier Transform technique. However, more analysis is necessary for addressing the sampling issues.
For current WAZ data processing, six azimuth sectors are output (see Huang et al., 2010). Thus, the migration output is oversampled in the azimuth angle domain, which does not cause a problem when the velocity model provides flat CIGs. On the other hand, the reflection angle is usually sampled in 1° to 2° increments. Sampling can be an issue when generating 3D ADCIGs. As will be discussed later, the events in the shallow ADCIGs are poorly sampled on the near angles and are better sampled on the far angles. In the deep part, the ADCIGs are generally oversampled. Thus, the gathers look normal when the velocity model is close to the real one.
However, when the velocity is off too much from the real velocity and the migrated events show curvatures on the ADCIGs, the amplitudes on the far angles are much attenuated with big angle intervals. As a result, the automatic event picking process may fail to pick the far angle curvatures for a further velocity update. Thus, there is a need to improve the signal-to-noise ratio (S/N) in RTM 3D ADCIGs. Accordingly, it would be desirable to provide systems and methods that avoid the afore-described problems and drawbacks.